Chapter 02 Section 07

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Chapter 02 Section 07

• Dividing Rational Numbers

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2-7 DIVIDING RATIONAL NUMBERS
OBJECTIVES
To divide rational numbers.
From prior knowledge To divide by a number is
the same thing as multiplying by its
reciprocal. All of the problems from this
section will follow this pattern 1) Turn the
divide statement into a multiply statement,
then 2) Use the exact same rules from last
section about multiplying numbers. Remember
The bar in a fraction is a symbol for division,
so means five divided by six.
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2-7 DIVIDING RATIONAL NUMBERS
This is essentially the same rule for multiplying
numbers. Like signs yield positive unlike
yield negative. Now for some examples.
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2-7 DIVIDING RATIONAL NUMBERS
EX1ß
EXAMPLE 1a Find each quotient. a. -75
(-15) b.
This can also be written as
Positive divided by negative yields a
negative. With that in mind, reduce the fraction.
You just reduce the fraction and keep the
negative divided by negative yields positive in
mind.
5
-9
EXAMPLE 1ß Find each quotient. a. -32
-8 b.
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2-7 DIVIDING RATIONAL NUMBERS
EX2ß
EXAMPLE 2a Find each quotient. a. b.
Rewrite as a multiplication problem.
Rewrite as a multiplication problem.
Multiply and reduce.
Multiply and reduce (remember sign.)
EXAMPLE 2ß Find each quotient. a. b.
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2-7 DIVIDING RATIONAL NUMBERS

• Now we have something called complex fractions.
• complex fraction - a fraction within a fraction
• These look hard but are fairly easy to do using
  the division-flip rule.
• Another means to solve these problems is the
  Sandwich Method.
• In the Sandwich Method, you take layer the
  complex fractions like this
• Multiply the bread layers for the new numerator.
• Multiply the PBJ layers for the new denominator.

numerator
denominator
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2-7 DIVIDING RATIONAL NUMBERS
EX3ß
EXAMPLE 3a Write each fraction in simplest
form. a. b.
Write the problem as a fraction over a fraction.
Write the problem as a fraction over a fraction.
Write as a multiplication problem.
Write as a multiplication problem.
Reduce.
No reduction necessary.
Multiply.
Multiply.
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2-7 DIVIDING RATIONAL NUMBERS
EXAMPLE 3ß Write each fraction in simplest
form. a. b.
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2-7 DIVIDING RATIONAL NUMBERS
To finish this section off, variables in division
problems need to be addressed. EXAMPLE 4a
Simplify
METHOD 1 Turn the division by four into a
multiplication by one-fourth.
METHOD 2 Divide both terms of the numerator by
the denominator, 4.
Distribute the 1/4.
Simplify.
Simplify.
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2-7 DIVIDING RATIONAL NUMBERS
EXAMPLE 4ß Simplify
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2-7 DIVIDING RATIONAL NUMBERS
HOMEWORK
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